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math.LO2024
On cohomology of locally profinite sets
Ko Aoki
We construct a locally profinite set of cardinality with infinitely many first cohomology classes of which any distinct finite product does not vanish. Building on this,…
math.KT2024
(Semi)topological -theory via solidification
Ko Aoki
Clausen--Scholze introduced the notion of solid spectrum in their condensed mathematics program. We demonstrate that the solidification of algebraic -theory recovers two known c…
math.CT2024
The smashing spectrum of sheaves
Ko Aoki
For an arbitrary -topos, we classify the smashing localizations in the -category of sheaves valued in derived vector spaces: Any of them is the restriction functor…